When wipers turn off or key is shut off wipers.

You need to check if the wiper motor is receiving voltage on the "park" circuit. If voltage is present, the motor is bad and needs to be replaced. If voltage
is not present, then the wiper switch needs to be replaced.

1999 old body style or new body style?

When the key is turned off, the wipers will stop where ever they happen to be (that is normal).

Thomas